I feel that I have a good idea of Japanese grammar, but I always get the nagging feeling that everything I write in Japanese is completely wrong. So I wrote this little thing to help. It is not a real letter to a real person --- just something I thought would be a little fun.

It's OK to use plain form in the middle of a sentence, like before ので and のに, and you don't need to use polite -te forms like なりまして. You can if you want, but it makes it really polite. What's mostly important is what comes at the end of the whole sentence.

Although I don't know the reason why, normally "普通な鉛筆" is not used in Japanese, and it is common to use "普通の鉛筆" instead of it.
"書いた"→"書いていました"

"消し事が易しかったけど"→"消す事は簡単だった(容易かった)けれど"

"先端は鈍くなったので"→"先端が鈍くなるので"
In this case, it is better not to use the past form, I think.

"鮮鋭" is a noun or a adjectival noun which is used for expressing "to see more clearly (for modifying a picture or something like this)". →"頻繁に削る必要がいつもありました。" (And "先鋭化する" means "be radicalized" or "become a radical".)
Note : "a pencil sharpener" is "鉛筆削り" in Japanese.

"先端がすり減らすのに、執筆の厚さも不変でこぎれい。"
Did you mean like this? ;"Even if the tip of it wears down, the thickness of the writing is steady and fine."
"先端がすり減っても、線の太さが変わらずに綺麗です。"

"しかし、弱点があります。芯は壊れやすい。"
It is grammatically correct, but to be elegant Japanese sentence, it might be better to avoid repeat of short sentence. →"しかし、シャープペンにも芯が折れやすいという欠点があります。"

"特に０．５ｍｍの物で"→"特に0.5mmのものは（では）"

だけど、鉛筆は短くなってシャープペンはしません。→ "だけど、鉛筆は短くなりますが、シャープペンはなりません。"
"Although a pencil will become shortened, a mechanical pencil is not so."

If you wanted to express; "This is the reason why I like a mechanical pencil."
→"それで（私は）シャープペンを好むわけです。"

I think it was almost well written as Japanese sentences. At least, I could easily understand what you wanted to say. So, I'm sorry, some of my pointing might be overcorrection.